A POD-Galerkin reduced order model for a LES filtering approach

TL;DR

This paper introduces a novel POD-Galerkin reduced order model for LES filtering in fluid dynamics, combining an Evolve-Filter algorithm with efficient finite volume methods, and incorporating pressure at the reduced level.

Contribution

It presents a new reduced order modeling approach that applies spatial filtering during snapshot collection and in the ROM, including pressure field modeling, for improved accuracy in LES simulations.

Findings

Accurate ROM for 2D and 3D flow past a cylinder at Re up to 100.

Effective parametric study on filtering radius for 2D case.

ROM results closely match full order model outcomes.

Abstract

We propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for a Leray model. For the implementation of the model, we combine a two-step algorithm called Evolve-Filter (EF) with a computationally efficient finite volume method. The main novelty of the proposed approach relies in applying spatial filtering both for the collection of the snapshots and in the reduced order model, as well as in considering the pressure field at reduced level. In both steps of the EF algorithm, velocity and pressure fields are approximated by using different POD basis and coefficients. For the reconstruction of the pressures fields, we use a pressure Poisson equation approach. We test our ROM on two benchmark problems: 2D and 3D unsteady flow past a cylinder at Reynolds number 0 <= Re <= 100. The accuracy of the reduced order model is assessed against results obtained with the full order model. For the 2D case, a parametric study with respect to the filtering radius is also presented.